We report a simple fiber sensor for measurement of high temperature with high sensitivity. The sensing head is a multimode-single mode-multimode (MM-SM-MM) fiber configuration formed by splicing a section of uncoated single mode fiber (SMF) with two short sections of multimode fibers (MMF) whose core is composed of pure silica. Because of the mode-field mismatch at the splicing points of the SMF with 2 sections of MMFs, as well as index matching between the core of the MMF and the cladding of the SMF, optical power from the lead-in fiber can be partly coupled to the cladding modes of the SMF through the MMF. The cladding modes of the SMF then re-coupled to the lead-out fiber, in the same fashion. Due to the effective index difference between the core and cladding modes, an interference pattern in the transmission spectrum of the proposed device was obtained. The interference pattern was found to shift to the longer wavelength region with respect to temperature variation. The temperature sensor can measure temperature stably up to more than 900 °C with sensitivity of 0.088 nm/°C.
©2008 Optical Society of America
Measurement of temperature using fiber optics has been extensively investigated using various techniques based on fiber devices . Among them, the use of Fiber Bragg gratings (FBG) [2–3] is particularly attractive for distributed sensing, but they suffer from limited temperature-induced spectral displacements (∼0.01 nm/°C) and need isolators to prevent back reflections. The use of long-period fiber gratings (LPFG) for a temperature sensor, which exhibit higher sensitivity (∼0.1 nm/°C) and low back reflection, may cause undesirable changes of the spectral response due to the high bending sensitivity . Alternative technique is the use of polarization maintaining (PM) fiber based temperature sensors, such as a Sagnac loop, which offers advantages such as easy manufacture, flexibility, and stability [5,6]. However, those temperature fiber sensors mentioned above have their disadvantages. Typical fiber sensor based on PM fibers requires bulky components such as polarization controller or polarizers and impractical for distributed sensing. On the other hand, temperature fiber sensors based on fiber grating might not operate at high temperature due to the tendency of being erased. A fiber sensor even using special FBGs in which intensive UV exposures cause negative index changes or physical damages  might operate in the temperature range over 500°C, but should not be more than 900°C . Surface relief FBG sensor, which was fabricated by etching a grating into the flat side of a D-shaped optical fiber, has been used for very high-temperature (about 1100°C) sensing . Since the grating is formed by physically changing the fiber geometry, it will not be erased under high temperatures. However, the fabrication process of the surface relief grating is rather complex, and the grating is fragile.
Recently there have been reports on utilizing the interference between guided modes of a MMF for temperature fiber sensors [10,11]. Compared with schemes using fiber gratings or PM fibers, MMF based temperature fiber sensors offer advantages such as low-cost and high temperature operation. However, usually the demonstrated temperature sensors based on conventional MMF has low temperature sensitivity of around 0.01 nm/°C . We believed that the low temperature sensitivity is due to the fact that the guided modes involved in the interference propagating primarily in the same core and therefore have very similar thermal coefficients. To improve the temperature sensitivity of MM fiber based sensor, long section of graded-index MMF could be used  but the sensitivity was still low (∼0.05 nm/°C) and the high temperature operation was not demonstrated.
In this paper, we propose and experimentally demonstrate a simple, low-cost, high temperature operation and high sensitivity fiber temperature sensor using the MM-SM-MM fiber configuration. Instead of using the interference between guided modes of a MM fiber for temperature sensing like the work in Refs 10 and 11, we used the interference between the core mode and the cladding modes of a SMF sandwiched between two short sections of MMFs which play the role as the mode couplers in our scheme. The proposed temperature sensor therefore can have much better sensitivity due to the large difference of thermal coefficients of the core mode and cladding modes, yet able to operate at high-temperature thanks to its non-grating configuration. Previously Villatoro et. al.  have demonstrated a refractive index sensor by splicing a section of uncoated SMF with 2 lead-in and lead-out MMFs in which the cladding modes of the SMF were excited through the large core diameter mismatch. However, the sensor operates based on the variable transmitted power with respect to the variation of ambient index since the interference pattern was not obtained in that experiment. In our work, using single mode lead-in and lead-out fibers and very short sections of MM fiber as the mode couplers, clear interference pattern were obtained with the MM-SMMM fiber structure. Inhomogeneous interference patterns confirm the excitement of cladding modes and analysis of the interference patterns for several interferometers with different lengths show that even though several cladding modes of the SM fiber were excited, typically one high-order cladding mode was dominant and mainly interfered with the core mode. The proposed temperature sensor based on MM-SM-MM fiber configuration can measure temperature up to more than 900°C with sensitivity of 0.088 nm/°C.
2. Schematic diagram of the sensing head and its principle of operation
The MM-SM-MM fiber configuration is shown in Fig. 1. A section of an uncoated SM fiber was spliced with two short sections of the same MM fiber. The fibers used in our experiment are Samsung single mode fiber (step index profile, core diameter ∼ 9 μm) and Thorlabs multimode fiber AFS 50/125Y (pure silica core with suppresed inner cladding, core diameter ∼ 50 μm). The operation principle of the device can be explained as follows: Assume that light is launched into the first MM fiber (MF 1) through a lead-in SMF as shown in Fig. 1. At the MF1-SMF splice point, part of the power can be coupled to the cladding modes of the SM fiber due to the mode field mismatch. It this case, the pure silica core of the MMFs used in our experiment is matched with the refractive index of the SMF fiber and therefore along with the large core diameter mismatch guarantee for the excitement of cladding modes of the SMF. It is different from the work in Ref 13 in which only the core modes LP01 and LP11 could be excited through a small misalignment between 2 single mode fibers and a small core fiber stub. Similarly, at the SMF-MF2 splice point, partly the cladding modes of the SMF will be again coupled to the guided modes of the MF2, along with the core mode of the SMF and consequently coupled into the fundamental mode of the lead-out fiber. Because of the refractive index differences between the SMF cladding/core modes, an interference pattern could be expected by measuring the transmission spectrum of the device. Here the lengths of the two MM fiber sections were chosen to be as short as possible so that the phase differences between their guided modes are negligible. Possible interference patterns formed by the interactions between higher order modes of the MM fiber should have very large free spectral range (FSR) and therefore the interference fringes might not fall into the measured wavelength range.
The phase difference between the core and the cladding modes after propagating through the length L of the SM fiber can be easily written as:
where Δnmeff is the effective refractive index difference between the core mode and the mth cladding modes. λ is the signal wavelength in vacuum. From Eq. (1), the wavelength separation between 2 interference minima (the FSR) can be approximated as:
It can be seen that the FSR will increase as the interferometer length L decreases. On the other hand, when a variation of temperature is applied, because of the different thermo-optic dependence of the effective refractive indices of the core and the cladding modes, δn eff must be changed and consequently the interference fringes will shift.
Several interferometers with different lengths were fabricated and their transmission spectra with L = 55 mm, 40 mm and 10 mm are shown in Fig. 2. The splicing condition was the standard automatic mode. As can be seen in Fig. 2, interference patterns were clearly obtained. Their inhomogeneous spectra confirmed for the excitement of the cladding modes since there must be more than 2 modes (2 arms) involved in an inhomogeneous interference pattern. As the only two supported modes in a short length of SMF fiber are the LP01 and LP11 modes , cladding modes of the SMF must have been excited and have participated in the interference. It is observed that when we applied the index matching oil to remove the cladding modes, the interference did not fully disappear but remained a very homogeneous interference pattern from the interference of the LP01 and LP11 core modes. However this interference has very small extinction ratio of approximately 3dB, similar to the results in  but much smaller than that in the case of no index matching oil. It is therefore believed that the cladding modes were excited much more strongly than the higher order core mode LP11 was.
One characteristic of the interference patterns is that in all three cases, despite the fact that the MM-SM-MM structure theoretically has no mechanism preventing the excitement of many cladding modes, a nearly-defined FSR was always obtained. Therefore, it can be assumed that practically only one cladding mode is dominantly excited. This dominant cladding mode interferes with the core mode to form the main interference pattern. Other cladding modes should also be excited but very weakly and therefore their interference with the core modes or other cladding modes will slightly modulate the main interference pattern.
In order to examine the assumption above, the wavelength spectra in Fig. 2 were Fourier transformed to get the spatial frequency. The result is shown in Fig. 3. Following the analysis in , the relation between the spatial frequency and the interferometer length as well as the differential modal group index was given as:
where L is the length of the single mode fiber, λ0 is center wavelength, ξ is spatial frequency and eff Δm is the differential modal group index. From Eq. (3), it can be seen that the spatial frequency ξ is proportional to both the interferometer length L and the differential modal group index Δmeff. For a fixed length, a smaller ξ corresponds to a smaller Δmeff which means a lower-order cladding mode . On the other hand, for a fixed Δmeff (a fixed cladding mode), ξ will decrease as the interferometer length L decreases. It can be seen in Fig. 3 that, for all three of fabricated interferometers with different lengths, there is indeed one dominantly excited cladding mode, along with other weakly excited ones. Take the case of L = 55 mm as an example. Besides the mainly excited cladding mode ξ =0.125 #/nm, there are also other weakly excited cladding mode whose orders are lower because their spatial frequencies are smaller, for example the notable low-order cladding mode located at ξ =0.017 #/nm. In all three cases, it can be seen that the strongly excited cladding mode is always the high order mode while the weakly excited ones are in low-order. The low order cladding mode should have effective indices much closer to that of the core mode, and therefore the FSRs of their interferences with the core mode would be much larger than that of the main interference. Those interferences modify slightly the envelope of the main interference as shown in Fig. 2. However, in case L = 10 mm, the effect of other lower order cladding mode excitement are too small (too large FSR) to be observed in the spectrum.
In the idea case where the lengths of the MF1 and MF2 are perfectly fixed during the fabrication of interferometers with different lengths, because the differential modal group indices (corresponding to specific cladding modes) must be the same as the excitement of cladding modes is not dependent on the interferometer length, all spatial spectra would maintain the same but linearly shift to the smaller value region according with respect to the interferometer length as shown in Eq. (3) as well as the experimental data in Ref 14, where two collapsed regions on a photonic crystal fiber with precisely controlled lengths were used as the mode couplers, The reason for the different spectra corresponding to the 3 interferometer lengths shown in Fig. 3 is attributed to the variation in the lengths of the MMF sections due to the instrument limits, slightly different lengths of the MMF could give rise to excitement of some other cladding modes because the length of the MMFs, for example MF1, determines the transverse field distribution at the interface MF1-SMF and thus determine the coupling strengths of MMF core modes to the SMF cladding/core modes.
Theoretically, the interference of the MM-SM-MM structure must include all the possible excited modes of the SMF, namely, the interferences between excited cladding modes, the interference between the core modes and finally the interferences between the cladding modes and the core modes. Given the length of the interferometer is known, this can be done as one calculate all of the excited modes of the SMF and make a superposition of all constitute components of the final interference. In general, all of the excited modes can be determined through calculation of coupling coefficients using the overlap integrals, first from the input field of the lead-in fiber to the MF1 , and then from the excited modes of the MF1 to the core modes and cladding modes of the SMF which can be calculated using the three-layer model [16,17]. However, the calculation is not within the scope of this paper as we unfortunately do not have sufficient specification on the purchased MMF. Because the fiber is a pure silica core with suppressed finite inner cladding whose diameter is unknown. It is required to have knowledge on the inner cladding diameter for calculation of the transverse field distribution of the core modes of MMF.
3. Measurement of high temperature with high sensitivity using the MM-SM-MM fiber configuration
The MM-SM-MM fiber configuration with L = 10 mm was used as the sensing head for our temperature sensor. As explained previously in this paper, in comparison with a temperature fiber sensor using the interference between guided core modes of a conventional MMF, one can expect better sensitivity utilizing the interference between the core mode and the cladding modes (propagating in different media which means significantly different thermal coefficients) of the SMF for temperature sensing, like the case of using a LPFG based temperature sensor. However, because there is no such fiber gratings involved with the MMSM- MM fiber configuration, we can also expect the device to operate at high temperature, like a MMF based temperature sensor.
The sensing head was put into a high temperature furnace whose temperature error is ± 2°C for temperature measurement. We chose the wavelength dip marked as DS in Fig. 2(c) as the spectral indicator for the temperature sensing because it has largest dynamic range in wavelength domain in our experiment. In order to remove the effect of fiber coating burned during the course of applying temperature, which might give undesirable strain on the sensing head, as well as to examine whether the dopant diffusion could seriously deteriorate the transmission spectrum of the devices, we first increased the temperature to more than 900 °C and then cool down to 30 °C to make sure that the coating material was burned out. The interference fringes were found to just slightly shift to the longer wavelength region after the heat treatment but its interference pattern was still well maintained. After that the temperature was gradually increased up to more than 900 °C while the positions of the dip DS were recorded. The result is shown in Fig. 4. As expected, the proposed sensor measured temperature up to more than 900 °C with a temperature of 0.088 nm/°C, almost same as that of a temperature sensor using LPFG  but an order of magnitude higher than that of temperature fiber sensors using conventional MMF . The inset shows the position of the dip DS at several temperatures. It is clear that there was no serious deterioration of the spectrum at high temperature, the dip DS shifted linearly to the longer wavelength region. However, it should be noted that fringe contrast of the dip DS was changed back and forth with respect to temperature, it gradually decreased as the temperature approached 600 °C but then increased again as the temperature increased up to 900 °C.
This paper presented interference pattern obtained by using the MM-SM-MM fiber configuration and applied the newly demonstrated interferometer to temperature fiber sensor. The temperature fiber sensor can be said to combine the advantages of a conventional MMF based temperature sensor and an LPFG based temperature sensor as it has a sensitivity of 0.088 nm/°C, and is able to measure high temperature stably up to 900 °C. It should be noted that the fiber sensor can also modified to operate in the reflection mode by placing a deposited mirror at one end of the SMF. Finally, it is very cost effective as the sensing head is composed of just few centimeters of commercially available optical fibers.
This research was partially supported by Telemetrics Project (1001678) and GIST Top Brand Project “Photonics 2020“, Ministry of Science and Technology, Republic of Korea.
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